Three-Dimensional Tracking of Interfacial Hopping Diffusion

Theoretical predictions have suggested that molecular motion at interfaces—which influences processes including heterogeneous catalysis, (bio)chemical sensing, lubrication and adhesion, and nanomaterial self-assembly—may be dominated by hypothetical “hops” through the adjacent liquid phase, where a diffusing molecule readsorbs after a given hop according to a probabilistic “sticking coefficient.” Here, we use three-dimensional (3D) single-molecule tracking to explicitly visualize this process for human serum albumin at solid-liquid interfaces that exert varying electrostatic interactions on the biomacromolecule. Following desorption from the interface, a molecule experiences multiple unproductive surface encounters before readsorption. An average of approximately seven surface collisions is required for the repulsive surfaces, decreasing to approximately two and a half for surfaces that are more attractive. The hops themselves are also influenced by long-range interactions, with increased electrostatic repulsion causing hops of longer duration and distance. These findings explicitly demonstrate that interfacial diffusion is dominated by biased 3D Brownian motion involving bulk-surface coupling and that it can be controlled by influencing short- and long-range adsorbate-surface interactions.

Figure 1

(a) A standard wide-field microscope body was equipped with a Double-Helix SPINDLE module to implement DH PSF imaging. (b) Two-dimensional projection of a trajectory. (c) Actual 3D motion for the trajectory shown in (b). To guide the eye, the red spheres indicate steps for the polymer in solution while the black ones denote steps at the surface. The inset shows the corresponding trace of $z$ position vs time.

Figure 2

(a),(b) Representative trajectories for HSA on a ${\mathrm{NH}}_2$-modified FS surface. The inset shows the corresponding trace of $z$ position vs time. (c) Mean-squared displacement vs lag time for HSA on surfaces with varying adsorbate-surface interactions. The subdiffusive scaling exponents are annotated on the right.

Figure 3

Apparent sticking coefficient of HSA on different surfaces.

Figure 4

(a) Hop-length distributions during flights for HSA on surfaces with varying surface-adsorbate interactions. (b) The cumulative probability of return time between consecutive surface encounters. The symbols denote the experimental data on different surfaces, and the solid lines indicate the simulation results described in the main text. The gray line in (b) represents the result of simulated Brownian motion.

Figure 5

Distribution of waiting times between flights for HSA on different surfaces. The symbols denote the experimental data, and the solid lines indicate power-law fits in the range of $0.5–5\mu \mathrm{m}$. The scaling exponents $\alpha$ obtained using an equation described in the main text are annotated on the right.